Safe MPC Alignment with Human Directional Feedback

In safety-critical robot planning or control, manually specifying safety constraints or learning them from demonstrations can be challenging. In this paper, we propose a certifiable alignment method for a robot to learn a safety constraint in its model predictive control (MPC) policy with human online directional feedback. To our knowledge, it is the first method to learn safety constraints from human feedback. The proposed method is based on an empirical observation: human directional feedback, when available, tends to guide the robot toward safer regions. The method only requires the direction of human feedback to update the learning hypothesis space. It is certifiable, providing an upper bound on the total number of human feedback in the case of successful learning of safety constraints, or declaring the misspecification of the hypothesis space, i.e., the true implicit safety constraint cannot be found within the specified hypothesis space. We evaluated the proposed method using numerical examples and user studies in two developed simulation games. Additionally, we implemented and tested the proposed method on a real-world Franka robot arm performing mobile water-pouring tasks in a user study. The simulation and experimental results demonstrate the efficacy and efficiency of our method, showing that it enables a robot to successfully learn safety constraints with a small handful (tens) of human directional corrections.

How Can LLM Guide RL? A Value-Based Approach

Reinforcement learning (RL) has become the de facto standard practice for sequential decision-making problems by improving future acting policies with feedback. However, RL algorithms may require extensive trial-and-error interactions to collect useful feedback for improvement. On the other hand, recent developments in large language models (LLMs) have showcased impressive capabilities in language understanding and generation, yet they fall short in exploration and self-improvement capabilities for planning tasks, lacking the ability to autonomously refine their responses based on feedback. Therefore, in this paper, we study how the policy prior provided by the LLM can enhance the sample efficiency of RL algorithms. Specifically, we develop an algorithm named LINVIT that incorporates LLM guidance as a regularization factor in value-based RL, leading to significant reductions in the amount of data needed for learning, particularly when the difference between the ideal policy and the LLM-informed policy is small, which suggests that the initial policy is close to optimal, reducing the need for further exploration. Additionally, we present a practical algorithm SLINVIT that simplifies the construction of the value function and employs subgoals to reduce the search complexity. Our experiments across three interactive environments ALFWorld, InterCode, and BlocksWorld demonstrate that our method achieves state-of-the-art success rates and also surpasses previous RL and LLM approaches in terms of sample efficiency. Our code is available at https://github.com/agentification/Language-Integrated-VI.

Adaptive Contact-Implicit Model Predictive Control with Online Residual Learning

The hybrid nature of multi-contact robotic systems, due to making and breaking contact with the environment, creates significant challenges for high-quality control. Existing model-based methods typically rely on either good prior knowledge of the multi-contact model or require significant offline model tuning effort, thus resulting in low adaptability and robustness. In this paper, we propose a real-time adaptive multi-contact model predictive control framework, which enables online adaption of the hybrid multi-contact model and continuous improvement of the control performance for contact-rich tasks. This framework includes an adaption module, which continuously learns a residual of the hybrid model to minimize the gap between the prior model and reality, and a real-time multi-contact MPC controller. We demonstrated the effectiveness of the framework in synthetic examples, and applied it on hardware to solve contact-rich manipulation tasks, where a robot uses its end-effector to roll different unknown objects on a table to track given paths. The hardware experiments show that with a rough prior model, the multi-contact MPC controller adapts itself on-the-fly with an adaption rate around 20 Hz and successfully manipulates previously unknown objects with non-smooth surface geometries.

Identifying Reaction-Aware Driving Styles of Stochastic Model Predictive Controlled Vehicles by Inverse Reinforcement Learning

The driving style of an Autonomous Vehicle (AV) refers to how it behaves and interacts with other AVs. In a multi-vehicle autonomous driving system, an AV capable of identifying the driving styles of its nearby AVs can reliably evaluate the risk of collisions and make more reasonable driving decisions. However, there has not been a consistent definition of driving styles for an AV in the literature, although it is considered that the driving style is encoded in the AV's trajectories and can be identified using Maximum Entropy Inverse Reinforcement Learning (ME-IRL) methods as a cost function. Nevertheless, an important indicator of the driving style, i.e., how an AV reacts to its nearby AVs, is not fully incorporated in the feature design of previous ME-IRL methods. In this paper, we describe the driving style as a cost function of a series of weighted features. We design additional novel features to capture the AV's reaction-aware characteristics. Then, we identify the driving styles from the demonstration trajectories generated by the Stochastic Model Predictive Control (SMPC) using a modified ME-IRL method with our newly proposed features. The proposed method is validated using MATLAB simulation and an off-the-shelf experiment.

Task-Driven Hybrid Model Reduction for Dexterous Manipulation

In contact-rich tasks, like dexterous manipulation, the hybrid nature of making and breaking contact creates challenges for model representation and control. For example, choosing and sequencing contact locations for in-hand manipulation, where there are thousands of potential hybrid modes, is not generally tractable. In this paper, we are inspired by the observation that far fewer modes are actually necessary to accomplish many tasks. Building on our prior work learning hybrid models, represented as linear complementarity systems, we find a reduced-order hybrid model requiring only a limited number of task-relevant modes. This simplified representation, in combination with model predictive control, enables real-time control yet is sufficient for achieving high performance. We demonstrate the proposed method first on synthetic hybrid systems, reducing the mode count by multiple orders of magnitude while achieving task performance loss of less than 5%. We also apply the proposed method to a three-fingered robotic hand manipulating a previously unknown object. With no prior knowledge, we achieve state-of-the-art closed-loop performance in less than five minutes of online learning.

Enforcing Hard Constraints with Soft Barriers: Safe Reinforcement Learning in Unknown Stochastic Environments

It is quite challenging to ensure the safety of reinforcement learning (RL) agents in an unknown and stochastic environment under hard constraints that require the system state not to reach certain specified unsafe regions. Many popular safe RL methods such as those based on the Constrained Markov Decision Process (CMDP) paradigm formulate safety violations in a cost function and try to constrain the expectation of cumulative cost under a threshold. However, it is often difficult to effectively capture and enforce hard reachability-based safety constraints indirectly with such constraints on safety violation costs. In this work, we leverage the notion of barrier function to explicitly encode the hard safety constraints, and given that the environment is unknown, relax them to our design of \emph{generative-model-based soft barrier functions}. Based on such soft barriers, we propose a safe RL approach that can jointly learn the environment and optimize the control policy, while effectively avoiding unsafe regions with safety probability optimization. Experiments on a set of examples demonstrate that our approach can effectively enforce hard safety constraints and significantly outperform CMDP-based baseline methods in system safe rate measured via simulations.

Learning multi-robot coordination from demonstrations

This paper develops a Distributed Differentiable Dynamic Game (DDDG) framework, which enables learning multi-robot coordination from demonstrations. We represent multi-robot coordination as a dynamic game, where the behavior of a robot is dictated by its own dynamics and objective that also depends on others' behavior. The coordination thus can be adapted by tuning the objective and dynamics of each robot. The proposed DDDG enables each robot to automatically tune its individual dynamics and objectives in a distributed manner by minimizing the mismatch between its trajectory and demonstrations. This process requires a new distributed design of the forward-pass, where all robots collaboratively seek Nash equilibrium behavior, and a backward-pass, where gradients are propagated via the communication graph. We test the DDDG in simulation with a team of quadrotors given different task configurations. The results demonstrate the capability of DDDG for learning multi-robot coordination from demonstrations

Learning Linear Complementarity Systems

This paper investigates the learning, or system identification, of a class of piecewise-affine dynamical systems known as linear complementarity systems (LCSs). We propose a violation-based loss which enables efficient learning of the LCS parameterization, without prior knowledge of the hybrid mode boundaries, using gradient-based methods. The proposed violation-based loss incorporates both dynamics prediction loss and a novel complementarity - violation loss. We show several properties attained by this loss formulation, including its differentiability, the efficient computation of first- and second-order derivatives, and its relationship to the traditional prediction loss, which strictly enforces complementarity. We apply this violation-based loss formulation to learn LCSs with tens of thousands of (potentially stiff) hybrid modes. The results demonstrate a state-of-the-art ability to identify piecewise-affine dynamics, outperforming methods which must differentiate through non-smooth linear complementarity problems.

Safe Pontryagin Differentiable Programming

We propose a Safe Pontryagin Differentiable Programming (Safe PDP) methodology, which establishes a theoretical and algorithmic safe differentiable framework to solve a broad class of safety-critical learning and control tasks -- problems that require the guarantee of both immediate and long-term constraint satisfaction at any stage of the learning and control progress. In the spirit of interior-point methods, Safe PDP handles different types of state and input constraints by incorporating them into the cost and loss through barrier functions. We prove the following fundamental features of Safe PDP: first, both the constrained solution and its gradient in backward pass can be approximated by solving a more efficient unconstrained counterpart; second, the approximation for both the solution and its gradient can be controlled for arbitrary accuracy using a barrier parameter; and third, importantly, any intermediate results throughout the approximation and optimization are strictly respecting all constraints, thus guaranteeing safety throughout the entire learning and control process. We demonstrate the capabilities of Safe PDP in solving various safe learning and control tasks, including safe policy optimization, safe motion planning, and learning MPCs from demonstrations, on different challenging control systems such as 6-DoF maneuvering quadrotor and 6-DoF rocket powered landing.

Learning from Incremental Directional Corrections

This paper proposes a technique which enables a robot to learn a control objective function incrementally from human user's corrections. The human's corrections can be as simple as directional corrections -- corrections that indicate the direction of a control change without indicating its magnitude -- applied at some time instances during the robot's motion. We only assume that each of the human's corrections, regardless of its magnitude, points in a direction that improves the robot's current motion relative to an implicit objective function. The proposed method uses the direction of a correction to update the estimate of the objective function based on a cutting plane technique. We establish the theoretical results to show that this process of incremental correction and update guarantees convergence of the learned objective function to the implicit one. The method is validated by both simulations and two human-robot games, where human players teach a 2-link robot arm and a 6-DoF quadrotor system for motion planning in environments with obstacles.